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17 January, 01:40

The carnival ride has a 2.0m radius and rotates 1.1 times persecond.

a. Find the speed of a rider.

b. Find the centripetal acceleration of a rider.

c. What produces this acceleration?

d. When the floor drops down riders are held up byfriction. What coefficient of friction is needed to keep theriders from slipping?

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Answers (1)
  1. 17 January, 01:45
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    a) v = 13.8 m / s, b) a = 95.49 m / s², c) a force that goes to the center of the carnival ride and d) μ = 0.10

    Explanation:

    For this exercise we will use the angular kinematics relationships and the equation that relate this to the linear kinematics

    a) reduce the magnitudes to the SI system

    w = 1.1 rev / s (2pi rad / 1rev) = 6.91 rad / s

    The equation that relates linear and angular velocity is

    v = w r

    v = 6.91 2

    v = 13.8 m / s

    b) centripetal acceleration is given by

    a = v² / r = w² r

    a = 6.91² 2

    a = 95.49 m / s²

    c) this acceleration is produced by a force that goes to the center of the carnival ride

    d) Here we use Newton's second law

    fr - W = 0

    fr = W

    μ N = mg

    Radial shaft

    N = m a

    N = m w² r

    μ m w² r = m g

    μ = g / w² r

    μ = 9.8 / 6.91² 2

    μ = 0.10
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